Every continuous function is
Area bounded by the curve xy^{2} = a^{2} (a  x) and yaxis is
Let f(x) = [cos x + sin x], 0 < x < 2π where [x] denotes the greatest integer less than or equal to x. The number of points of discontinuity of f(x) is
We know that [x] is discontinuous at integral values of x.
Equation of the circle having diameters 2x  3y = 5 and 3x  4y = 7 and radius 8 is
Coordinates of two points are A(1,0) and B(1,0) and Q is a point which satisfies AQBQ = + 1. The locus of the point Q is
The term independent of x in the expansion of ((2x)  (3/x))^{6} is
The equation of tangent at point (1,2) to the parabola y^{2}=4x is
The number of solutions of the equation
The area bounded by the curve y=sinx, y=0, x=0 and x=(π/2) is
The family of curves, in which the subtangent at any point to any curve is double the abscissa, is given by
If the matrix is singular one, then λ is
∫x sec^{2}x dx=
If A and B are 2 x 2 matrices then (A+B)^{2}=
The ratio of the altitude of the cone of greatest volume which can be inscribed in a given sphere to the diameter of the sphere is
The mean of 3, y, 4, x, 10, is 5, then y =
The inverse of matrix
In a certain distribution, the following results were obtained , Median = 48, Coefficient of skewness = 0.3.
What is the value of standard deviation?
The angle between lines y^{2}sin^{2}θxysin^{2}θ+x^{2}(cos^{2}θ1) = 1 is
Three identical dice are rolled. The probability that the same number will appear on each of them is
If the sides of a triangle are proportional to the cosines of the opposite angles then the triangle is
If the difference between the corresponding roots of x^{2} + ax + b = 0 and x^{2} + bx + a = 0 is same and a ≠ b, then
If A.M. between two numbers is 5 and their G.M. is 4, then their H.M. is
If x, y and z respectively represent AM, GM and HM between two numbers a and b, then
y^{2} = xz
Here x = 5, y = 4
then 16 = 5 x z
z = 16/5
The number of 4digit even numbers that can be formed using 0, 1, 2, 3, 4, 5, 6 without repetition is
Each even number must have 0, 2, 4 or 6 in is units place
Here total number of digits = 7
When 0 occurs at units place there is no restriction on other places and when 2 or 4 occurs at units place there is restriction on thousands' place as 0 can not be put at thousands' place
Case I When 0 occurs at units place:
∴ The number of numbers formed in this case
Case II. When 0 does not occur at units place:
The units' place can be filled up by any one of the three digits 2, 4 and 6 in 3 ways
∴ The number of numbers formed in this case
∴ The required number = 120 + 300 = 420
A condition for a function y = f (x) to have an inverse is that it should be
The derivative of is given by
A line passing through point A(5,4) meet other three lines x + 3y + 2 = 0, 2x + y + 4 = 0 and x  y  5 = 0 at B, C and D respectively. If (15/AB )^{2} + (10/AC)^{2} = (6/AD)^{2}, then the equation of line is
Equation of any line through A(5, 4) is
then the coordinates of any point on this line at a distance r from A are
(r cosθ  5, r sinθ  4)
If AB = r_{1}, AC = r_{2}, AD = r_{3}
then (r_{1} cosθ  5, r_{1} sinθ  4) lies on x + 3y + 2 = 0
⇒ r_{1} cosθ  5 + 3 (r_{1} sinθ  4) + 2 = 0
⇒ r_{1} (cosθ + 3 sinθ) = 15
Therefore according to the given condition
Hence the required equation of the line is
X follows a binomial distribution with parameters n = 6 and p. If 4 P (X = 4) = P (X = 2), then p =
The curve ye^{xy}+x=0 has a vertical tangent at the point
The equation 3sin^{2}x + 10cosx  6 = 0 is satisfied if
The minimum value of sin xcos x is
A tetrahedron has vertices at O (0,0,0), A(1,2,1), B(2,1,3) and C(1,1,2), then the angle between the faces OAB and ABC will be
If a=2i+jk, b=i+2j+k and c=ij+2k then a.(bxc)=
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